To compute \( 1 \frac{1}{6} \div \frac{1}{2} \), we first need to convert the mixed number \( 1 \frac{1}{6} \) into an improper fraction.
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Convert \( 1 \frac{1}{6} \): \[ 1 \frac{1}{6} = 1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \]
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Now, we rewrite the division operation: \[ \frac{7}{6} \div \frac{1}{2} \]
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Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{7}{6} \times \frac{2}{1} = \frac{7 \times 2}{6 \times 1} = \frac{14}{6} \]
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Now, simplify \( \frac{14}{6} \): \[ \frac{14}{6} = \frac{7}{3} \quad \text{(dividing both numerator and denominator by 2)} \]
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Convert \( \frac{7}{3} \) back to a mixed number: \[ 7 \div 3 = 2 \quad \text{(with a remainder of 1)} \] Thus, \( \frac{7}{3} = 2 \frac{1}{3} \).
So, the final answer is: \[ \boxed{2 \frac{1}{3}} \]
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